Chapter 4 - Vibration of Plates

Abstract

This chapter analyzes the vibration of thin plates. After reviewing the general plate equations, two situations are considered separately: (a) axial in-plane vibration of plates; and (b) flexural out-of-plane vibration of plates. Both rectangular coordinates and cylindrical coordinates are used, as appropriate. For rectangular plates, simplified solutions are derived for straight-crested axial and flexural vibrations and compared with the corresponding 1-D cases discussed in Chapter 3. General solutions for the 2-D flexural vibration of rectangular plates are given from the literature. The vibration of circular plates is treated in terms of Bessel functions. Closed-form solutions are derived for axisymmetric vibration of circular plates, to be used later in Chapter 9 for the analysis of PWAS resonators and in Chapter 10 for SHM analysis of electromechanical (E/M) impedance of circular PWAS transducers applied to circular plates.